1. ## calculus residue

hi everyone somebody knows to calculate the following residue of

$\displaystyle e^{-x z} \left(\text{Log}\left[\frac{1}{z}\right]\right)$ at z=0
using Mathematica or maple gives
0
$\displaystyle \text{Residue}\left[e^{-x z} \left(\text{Log}\left[\frac{1}{z}\right]\right),\{z,0\}\right]$ ==0 and using the definition of residue
$\displaystyle \text{Limit}\left[z \left(e^{-x z} \left(\text{Log}\left[\frac{1}{z}\right]\right)\right),z\to 0\right]$ gives 0 but i think it result is wrong.
thanks any help

2. ## Re: calculus residue

Originally Posted by capea
hi everyone somebody knows to calculate the following residue of

$\displaystyle e^{-x z} \left(\text{Log}\left[\frac{1}{z}\right]\right)$ at z=0
using Mathematica or maple gives
0
$\displaystyle \text{Residue}\left[e^{-x z} \left(\text{Log}\left[\frac{1}{z}\right]\right),\{z,0\}\right]$ ==0 and using the definition of residue
$\displaystyle \text{Limit}\left[z \left(e^{-x z} \left(\text{Log}\left[\frac{1}{z}\right]\right)\right),z\to 0\right]$ gives 0 but i think it result is wrong.
thanks any help
The Laurent expansion of the function $\displaystyle \ln \frac{1}{z} = - \ln z$ around $\displaystyle z=0$ doesn't exist , and the same is for its residue in $\displaystyle z=0$... the question has been discussed in...

http://www.mathhelpforum.com/math-he...st-167358.html

Kind regards

$\displaystyle \chi$ $\displaystyle \sigma$